Question

A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is ${60}^0$ and one of the fields has a magnitude of $1.2\times {10}^{-2}$T. If the dipole comes to stable equilibrium at an angle of ${30}^0$ with this field, then the magnitude of the field is

• A. $1.2\times {10}^{-4}$T
• B. $2.4\times {10}^{-4}$T
• C. $1.2\times {10}^{-2}$T
• D. $2.4\times {10}^{-2}$T

Answer 1

The correct option is C $1.2\times {10}^{-2}$T

Here, $\theta ={60}^0,B_1=1.2\times {10}^{-2}T$

${\theta }_1={30}^{0}and{\theta }_2={60}^0-{30}^0={30}^0$ in stable equilibrium,

torques due to two fields must be balanced i.e. $T_1=T_2$

$\Rightarrow M{B}_{1}sin{\theta }_1=M{B}_{2}sin{\theta }_2$

or $B_2=B_1\frac{sin{\theta }_1}{sin{\theta }_2}=B_2\frac{sin{30}^0}{sin{30}^0}=B_1=1.2\times {10}^{-2}T$